Guns, Swimming Pools, and Statistics

Which causes more accidental deaths:
guns or swimming pools?

Guns are portrayed as being very dangerous objects
that kill enormous numbers of children
every year.
Yes, guns are dangerous weapons, and they
should be kept securely locked away from children.
However, a swimming pool is far more likely
to cause the accidental death of a child.
How much more?
Can we estimate the relative probabilities?
Yes we can!

We need some basic figures:

Number of swimming pools in the U.S.

Number of privately owned firearms in the U.S.

Number of U.S. households with firearms.

Accidental deaths due to firearms.

Accidental deaths due to drowning in swimming pools.

Number of pools and hot tubs in the United States:

A Google search for "how many swimming pools in the U.S."
yields a number of pages with identical text claiming
that their data comes from a 2004 report by the
International Aquatic Foundation, although
the referenced URL
just leads to some domain-parking page.
The
Aquaticnet.com page
seems somewhat authoritative.
Those statistics, for 2004, are:

4,544,000

residential in-ground pools

3,535,000

residential above-ground pools

5,170,000

residential hot tubs

270,000

commercial swimming pools

That makes for a total of 13,519,000 pools and hot tubs,
or 8,349,000 for swimming pools alone.

Residential pools outnumber commercial or public
pools by a factor of about 30 to 1, so it will make little
difference whether we include non-residential pools or not.
I don't know how many non-residental hot tubs there are,
but I can't imagine that there are very many.
A city of a million people would have just a few hotels
with non-residential hot tubs.

The most recent CDC data I have found divides causes into
categories of "bathtub", "private pool", "public pool",
"unspecified pool", "natural water, including boating",
and "all other and unspecified."
I don't know where they put hot tubs.

Number of privately owned firearms in the U.S.:

The
Bureau of Alcohol, Tobacco, Firearms, and Explosives
estimated that there were 215 million privately owned
firearms in 1999 [1],
and the Bureau of Justice reported 72 million approved new
and used firearm transactions between 1999 and 2007 [2].
BATFE estimates an annual rise of 4.5 million [3],
which would indicate
219.5 million in 2000,
237.5 million in 2004 and
251 million in 2007.
However, the ownership is not evenly distributed.
A more useful value is the number of households
with at least one firearm.

Number of U.S. households with firearms:

A 1993 Gallup poll estimated that 49% of U.S. households
have at least one gun.
An article in the journal Injury Prevention
in 2004 estimated that it was 38% of households.
All these estimates are extrapolated from surveys of a few
hundred to a few thousand people.

The 2000 Census reported
a U.S. population of
"281.4 million people, of whom 273.6 million were
living in 105.5 million households."
I don't know who those other 7.8 million people not living
in households might be (military, college students,
and prisoners would be my best guess),
but 38% and 49% of that total means
40.1 to 51.7 million households with guns.

I am puzzled and disappointed by their listing of both
"Fatal Drowning" and "Non-Fatal Drowning."
CDC, learn to speak English!
Drowning is death by water, while
near drowning is almost dying because of water.
Similarly, when you receive a bad but non-fatal electrical
shock, what happened is that you were shocked.
If it actually kills you, then that is electrocution.

More useful data on drowning is listed in the CDC's
Drowning — United States, 2005—2009
report, part of their MMWR or
Morbidity and Mortality Weekly Report
of May 18, 2012 (vol 61, number 19, page 344-347).
To just list what actual speakers of the English language
would correctly call "drowning" (that's the fatal variety,
you see), the annual averages for 2005-2009 were:

Age in years

all ages

0-4

5-14

≥15

unknown

Drowning deaths

3881

513

252

3,107

9

That same report
has a graphic showing locations of drowning.
I printed the graphic and measured the segments to the nearest
millimeter.
From 0 to 100% was 74 millimeters, so I scaled all the segment
measures by a factor of 100/74 and rounded the result
to the nearest whole number percentage.
Those locations are:

Location of drowning

0-4 years

5-14 years

≥15 years

Bathtub

15%

5%

11%

Pool

50%

31%

11%

Natural water, including boating

15%

46%

58%

All other and unspecified

20%

18%

20%

Let's assume that the distribution of drowning locations
did not change significantly over the period from 2000 to 2009.
We can use this location information to calculate the
number of deaths due to accidental firearms discharge,
and to estimate with fairly high certainty the number of
drowning deaths in swimming pools only:

Age in years

0-4

5-14

≥15

Drowning deaths in swimming pools annually 2005-2009

257

78

342

Death by accidental firearm discharge in 2000

19

67

690

Also note that according to the State Farm insurance company
in 2011, about 183 children under the age of 15 are killed
every year in the U.S. by a car backing over them in the
driveway.
That's over twice the number killed by accidental firearms
discharges.
The U.S. Department of Transportation estimated
that driving while drowsy causes 71,000 injuries and
1,550 deaths per year in the U.S.
That's just about 40-45% of the number of drowning deaths and
twice the number of accidental firearms discharges deaths.
But before we ban cars, let's do some analysis.

The Numbers

Number

Measure or Annual Average

Year(s)

8,079,000

Residential swimming pools

2004

219,500,000

Privately owned firearms

2000

40,100,000

Households with guns (low estimate)

2000

51,700,000

Households with guns (high estimate)

2000

677

Americans killed by drowning in swimming pools

2005-2009

335

Children 0-14 killed by drowning in swimming pools

2005-2009

776

Americans killed by accidental discharge of firearms

2000

86

Children 0-14 killed by accidental discharge of firearms

2000

Now we can calculate rates.
Notice that firearms are far more common
than swimming pools.
We need to scale the death rates by the prevalence of
the underlying causes if we are going to estimate the
conditional probability
— given that
risky item X exists in a household, what is
the likelihood that it will lead to an accidental death?

Цар
Николай
II

You have to be careful when calculating or discussing
probability, especially when what you're really discussing
is conditional probability.
The probability of X given Y is very
different from the probability of Y given X.

For example: If you were a member of the Russian royal
family, then there would be a much higher than
usual likelihood that you had hemophilia.
But that does not make the converse true: Just because you
happen to have hemophilia does not mean that you are
probably Russian royalty!

Number

For the entire population

8.380

Swimming pool drowning deaths per
100,000 residential swimming pools

1.501—1.935

Accidental firearm deaths per
100,000 households with at least one firearm

0.354

Accidental firearm deaths per
100,000 firearms

If we calculate the rates per 100,000 instances of the risk,
the numbers will be a little easier to compare.
The estimates for gun-owning households is shown as a range,
as the number of those households is itself a range.
First, for the entire population, see the table at right:

And, for children less than fifteen years old see the table below:

Number

For children less than 15 years old

4.147

Swimming pool drowning deaths per 100,000 residential swimming pools

0.166—0.214

Accidental firearm deaths per 100,000 households with at least one firearm

0.039

Accidental firearm deaths per 100,000 firearms

So, having a swimming pool in a household is
something like 4.3 to 5.6 times as likely to lead
to an accidental death as having a firearm,
when we look at the numbers for all age groups.
For children less than 15, the difference is
more like 19 to 25 times as likely.

I was very surprised by these results!
I would have guessed that the accidental death rate for
drowning was higher, but not by the factor of
19 to 25 that we see for children!

According to a 2007 Department of Transportation study,
there were an estimated 254.4 million registered passenger
vehicles (cars, pickup trucks, SUVs and minivans)
in the United States.
The U.S. Census Bureau
estimates
114.8 million households in the U.S. in 2010, and an estimated
91.7% of these, or 105.3 million households, own at least one
passenger vehicle.
Doing the same math for what the State Farm insurance company
classifies as a "back-over accident", in which a child less
than 15 years of age is killed when a car backs over them,
usually in a driveway, we get:

Number

For children less than 15 years old

0.174

Back-over deaths per 100,000 households with at least one passenger vehicle

0.072

Back-over deaths per 100,000 passenger vehicles

So, while a passenger vehicle is
not nearly as dangerous as a swimming pool or hot tub, one of
them is still almost twice as likely to fatally back over
a child as a firearm is to accidentally shoot a child.
(0.072 versus 0.039 per 100,000)

Reverse gear: twice as likely as a gun to kill a child.

I looked into this after seeing it mentioned in
Freakonomics: A Rogue Economist Explores the
Hidden Side of Everything,
by Steven Levitt and Stephen Dubner.
It's a fascinating book — it's filled with surprising
explanations of just why things work the way they do.
I found it interesting that while one of their examples is
how a swimming pool is so much more likely to cause an
accidental death than a firearm,
they strongly questioned the statistical analysis and
conclusions of the standard pro-gun reference
More Guns, Less Crime.

Another interesting table in
Freakonomics
is the following one,
based on "Secular Trends of Violence, Evidence, and
Theoretical Interpretations" by the criminologist
Manuel Eisner,
Crime & Justice: A Review of Research 3 (2003),
also in
"Violence and the Rise of Modern Society",
Criminology in Cambridge, Oct 2003, pp 3-7:

Homicides per 100,000 people

England

Netherlands & Belgium

Scandinavia

Germany & Switzerland

Italy

13th/14th Century

23.0

47.0

—

37.0

56.0

15th Century

—

45.0

46.0

16.0

73.0

16th Century

7.0

25.0

21.0

11.0

47.0

17th Century

5.0

7.5

18.0

7.0

32.0

18th Century

1.5

5.5

1.9

7.5

10.5

19th Century

1.7

1.6

1.1

2.8

12.6

1900-1940

0.8

1.5

0.7

1.7

3.2

1950-1994

0.9

0.9

0.9

1.0

1.5

Also see
Steven Pinker's
The Better Angels of Our Nature:
Why Violence Has Declined,
which explains a number of historical trends.
And it was even worse in prehistoric times.
A cemetery in west-central Illinois dating from before
European contact contains 264 skeletons, of which 43
or 16.3% had died violently.
A prehistoric burying ground in British Columbia showed
that 20% of the people had died violently.
A Mesolithic era burial ground in southern Sweden showed
8.3% violent death rate.

Moving into the historic period, Pinker found even higher
homicide rates than in the above table from the 2003 study.
He found that English court records showed
that 14th century London had a homicide rate around
55 per 100,000, and Oxford's was 100 per 100,000.
In the 15th century, Amsterdam's homicide rate was about
50 per 100,000,
and in the 16th century, Italy's was 30 to 70 per 100,000.

Michael Wood's In Search of England
tells us that during the 13th century,
40% of all crime which came to court in
England was larceny, largely of farm stock.
20% was burglary (forced breaking and entering),
10% was robbery, and
homicide was the subject of nearly 20% of court cases!

Compare that to today's U.S., seen as a violent society,
where only about 0.5% of crimes are homicide.
London had 5 murders per year per 10,000 people back in the
13th century, while Miami
("murder capital of US" in 2001 when he wrote that book)
had 1.5.

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